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boringssl/include/openssl/bn.h
Brian Smith ec3cb3adbc Add |BN_mod_inverse_blinded| and use it in RSA blinding. 
Yo dawg I herd you like blinding so I put inversion blinding in your
RSA blinding so you can randomly mask your random mask.

This improves upon the current situation where we pretend that
|BN_mod_inverse_no_branch| is constant-time, and it avoids the need to
exert a lot of effort to make a actually-constant-time modular
inversion function just for RSA blinding.

Note that if the random number generator weren't working correctly then
the blinding of the inversion wouldn't be very effective, but in that
case the RSA blinding itself would probably be completely busted, so
we're not really losing anything by relying on blinding to blind the
blinding.

Change-Id: I771100f0ad8ed3c24e80dd859ec22463ef2a194f
Reviewed-on: https://boringssl-review.googlesource.com/8923
Reviewed-by: Adam Langley <agl@google.com>
Commit-Queue: Adam Langley <agl@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
2016-07-29 18:30:34 +00:00

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/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/* ====================================================================
* Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the Eric Young open source
* license provided above.
*
* The binary polynomial arithmetic software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#ifndef OPENSSL_HEADER_BN_H
#define OPENSSL_HEADER_BN_H
#include <openssl/base.h>
#include <openssl/thread.h>
#include <inttypes.h> /* for PRIu64 and friends */
#include <stdio.h> /* for FILE* */
#if defined(__cplusplus)
extern "C" {
#endif
/* BN provides support for working with arbitary sized integers. For example,
* although the largest integer supported by the compiler might be 64 bits, BN
* will allow you to work with numbers until you run out of memory. */
/* BN_ULONG is the native word size when working with big integers.
*
* Note: on some platforms, inttypes.h does not define print format macros in
* C++ unless |__STDC_FORMAT_MACROS| defined. As this is a public header, bn.h
* does not define |__STDC_FORMAT_MACROS| itself. C++ source files which use the
* FMT macros must define it externally. */
#if defined(OPENSSL_64_BIT)
#define BN_ULONG uint64_t
#define BN_BITS2 64
#define BN_DEC_FMT1 "%" PRIu64
#define BN_DEC_FMT2 "%019" PRIu64
#define BN_HEX_FMT1 "%" PRIx64
#elif defined(OPENSSL_32_BIT)
#define BN_ULONG uint32_t
#define BN_BITS2 32
#define BN_DEC_FMT1 "%" PRIu32
#define BN_DEC_FMT2 "%09" PRIu32
#define BN_HEX_FMT1 "%" PRIx32
#else
#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
#endif
/* Allocation and freeing. */
/* BN_new creates a new, allocated BIGNUM and initialises it. */
OPENSSL_EXPORT BIGNUM *BN_new(void);
/* BN_init initialises a stack allocated |BIGNUM|. */
OPENSSL_EXPORT void BN_init(BIGNUM *bn);
/* BN_free frees the data referenced by |bn| and, if |bn| was originally
* allocated on the heap, frees |bn| also. */
OPENSSL_EXPORT void BN_free(BIGNUM *bn);
/* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was
* originally allocated on the heap, frees |bn| also. */
OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn);
/* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the
* allocated BIGNUM on success or NULL otherwise. */
OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src);
/* BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation
* failure. */
OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src);
/* BN_clear sets |bn| to zero and erases the old data. */
OPENSSL_EXPORT void BN_clear(BIGNUM *bn);
/* BN_value_one returns a static BIGNUM with value 1. */
OPENSSL_EXPORT const BIGNUM *BN_value_one(void);
/* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the
* contents of |in| but with |flags| ORed into the flags field.
*
* Note: the two BIGNUMs share state and so |out| should /not/ be passed to
* |BN_free|. */
OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags);
/* Basic functions. */
/* BN_num_bits returns the minimum number of bits needed to represent the
* absolute value of |bn|. */
OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn);
/* BN_num_bytes returns the minimum number of bytes needed to represent the
* absolute value of |bn|. */
OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn);
/* BN_zero sets |bn| to zero. */
OPENSSL_EXPORT void BN_zero(BIGNUM *bn);
/* BN_one sets |bn| to one. It returns one on success or zero on allocation
* failure. */
OPENSSL_EXPORT int BN_one(BIGNUM *bn);
/* BN_set_word sets |bn| to |value|. It returns one on success or zero on
* allocation failure. */
OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value);
/* BN_set_negative sets the sign of |bn|. */
OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign);
/* BN_is_negative returns one if |bn| is negative and zero otherwise. */
OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn);
/* BN_get_flags returns |bn->flags| & |flags|. */
OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags);
/* BN_set_flags sets |flags| on |bn|. */
OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags);
/* Conversion functions. */
/* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as
* a big-endian number, and returns |ret|. If |ret| is NULL then a fresh
* |BIGNUM| is allocated and returned. It returns NULL on allocation
* failure. */
OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret);
/* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian
* integer, which must have |BN_num_bytes| of space available. It returns the
* number of bytes written. */
OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out);
/* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a
* big-endian integer. The integer is padded with leading zeros up to size
* |len|. If |len| is smaller than |BN_num_bytes|, the function fails and
* returns 0. Otherwise, it returns 1. */
OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in);
/* BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. */
OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in);
/* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex
* representation of |bn|. If |bn| is negative, the first char in the resulting
* string will be '-'. Returns NULL on allocation failure. */
OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn);
/* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by
* a '-' to indicate a negative number and may contain trailing, non-hex data.
* If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and
* stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and
* updates |*outp|. It returns the number of bytes of |in| processed or zero on
* error. */
OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in);
/* BN_bn2dec returns an allocated string that contains a NUL-terminated,
* decimal representation of |bn|. If |bn| is negative, the first char in the
* resulting string will be '-'. Returns NULL on allocation failure. */
OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a);
/* BN_dec2bn parses the leading decimal number from |in|, which may be
* proceeded by a '-' to indicate a negative number and may contain trailing,
* non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the
* decimal number and stores it in |*outp|. If |*outp| is NULL then it
* allocates a new BIGNUM and updates |*outp|. It returns the number of bytes
* of |in| processed or zero on error. */
OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in);
/* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in|
* begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A
* leading '-' is still permitted and comes before the optional 0X/0x. It
* returns one on success or zero on error. */
OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in);
/* BN_print writes a hex encoding of |a| to |bio|. It returns one on success
* and zero on error. */
OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a);
/* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */
OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a);
/* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is
* too large to be represented as a single word, the maximum possible value
* will be returned. */
OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn);
/* ASN.1 functions. */
/* BN_parse_asn1_unsigned parses a non-negative DER INTEGER from |cbs| writes
* the result to |ret|. It returns one on success and zero on failure. */
OPENSSL_EXPORT int BN_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret);
/* BN_parse_asn1_unsigned_buggy acts like |BN_parse_asn1_unsigned| but tolerates
* some invalid encodings. Do not use this function. */
OPENSSL_EXPORT int BN_parse_asn1_unsigned_buggy(CBS *cbs, BIGNUM *ret);
/* BN_marshal_asn1 marshals |bn| as a non-negative DER INTEGER and appends the
* result to |cbb|. It returns one on success and zero on failure. */
OPENSSL_EXPORT int BN_marshal_asn1(CBB *cbb, const BIGNUM *bn);
/* Internal functions.
*
* These functions are useful for code that is doing low-level manipulations of
* BIGNUM values. However, be sure that no other function in this file does
* what you want before turning to these. */
/* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or
* until |top| is zero. */
OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn);
/* bn_wexpand ensures that |bn| has at least |words| works of space without
* altering its value. It returns one on success or zero on allocation
* failure. */
OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, size_t words);
/* BIGNUM pools.
*
* Certain BIGNUM operations need to use many temporary variables and
* allocating and freeing them can be quite slow. Thus such opertions typically
* take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx|
* argument to a public function may be NULL, in which case a local |BN_CTX|
* will be created just for the lifetime of that call.
*
* A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called
* repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made
* before calling any other functions that use the |ctx| as an argument.
*
* Finally, |BN_CTX_end| must be called before returning from the function.
* When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from
* |BN_CTX_get| become invalid. */
/* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */
OPENSSL_EXPORT BN_CTX *BN_CTX_new(void);
/* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx|
* itself. */
OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx);
/* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future
* calls to |BN_CTX_get|. */
OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx);
/* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once
* |BN_CTX_get| has returned NULL, all future calls will also return NULL until
* |BN_CTX_end| is called. */
OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx);
/* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the
* matching |BN_CTX_start| call. */
OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx);
/* Simple arithmetic */
/* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a|
* or |b|. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
/* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may
* be the same pointer as either |a| or |b|. It returns one on success and zero
* on allocation failure. */
OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
/* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */
OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w);
/* BN_sub sets |r| = |a| - |b|, where |r| may be the same pointer as either |a|
* or |b|. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
/* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers,
* |b| < |a| and |r| may be the same pointer as either |a| or |b|. It returns
* one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
/* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on
* allocation failure. */
OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w);
/* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or
* |b|. Returns one on success and zero otherwise. */
OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx);
/* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on
* allocation failure. */
OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w);
/* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as
* |a|. Returns one on success and zero otherwise. This is more efficient than
* BN_mul(r, a, a, ctx). */
OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
/* BN_div divides |numerator| by |divisor| and places the result in |quotient|
* and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in
* which case the respective value is not returned. The result is rounded
* towards zero; thus if |numerator| is negative, the remainder will be zero or
* negative. It returns one on success or zero on error. */
OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem,
const BIGNUM *numerator, const BIGNUM *divisor,
BN_CTX *ctx);
/* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the
* remainder or (BN_ULONG)-1 on error. */
OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor);
/* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the
* square root of |in|, using |ctx|. It returns one on success or zero on
* error. Negative numbers and non-square numbers will result in an error with
* appropriate errors on the error queue. */
OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx);
/* Comparison functions */
/* BN_cmp returns a value less than, equal to or greater than zero if |a| is
* less than, equal to or greater than |b|, respectively. */
OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b);
/* BN_cmp_word is like |BN_cmp| except it takes its second argument as a
* |BN_ULONG| instead of a |BIGNUM|. */
OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG b);
/* BN_ucmp returns a value less than, equal to or greater than zero if the
* absolute value of |a| is less than, equal to or greater than the absolute
* value of |b|, respectively. */
OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
/* BN_equal_consttime returns one if |a| is equal to |b|, and zero otherwise.
* It takes an amount of time dependent on the sizes of |a| and |b|, but
* independent of the contents (including the signs) of |a| and |b|. */
OPENSSL_EXPORT int BN_equal_consttime(const BIGNUM *a, const BIGNUM *b);
/* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero
* otherwise. */
OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w);
/* BN_is_zero returns one if |bn| is zero and zero otherwise. */
OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn);
/* BN_is_one returns one if |bn| equals one and zero otherwise. */
OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn);
/* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */
OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w);
/* BN_is_odd returns one if |bn| is odd and zero otherwise. */
OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn);
/* Bitwise operations. */
/* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the
* same |BIGNUM|. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
/* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same
* pointer. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a);
/* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same
* pointer. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
/* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same
* pointer. It returns one on success and zero on allocation failure. */
OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a);
/* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a|
* is 2 then setting bit zero will make it 3. It returns one on success or zero
* on allocation failure. */
OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n);
/* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if
* |a| is 3, clearing bit zero will make it two. It returns one on success or
* zero on allocation failure. */
OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n);
/* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|,
* or zero if the bit doesn't exist. */
OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n);
/* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one
* on success or zero if |n| is greater than the length of |a| already. */
OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n);
/* Modulo arithmetic. */
/* BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error. */
OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
/* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */
#define BN_mod(rem, numerator, divisor, ctx) \
BN_div(NULL, (rem), (numerator), (divisor), (ctx))
/* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <=
* |rem| < |divisor| is always true. It returns one on success and zero on
* error. */
OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator,
const BIGNUM *divisor, BN_CTX *ctx);
/* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero
* on error. */
OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m, BN_CTX *ctx);
/* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be
* non-negative and less than |m|. */
OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m);
/* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero
* on error. */
OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m, BN_CTX *ctx);
/* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be
* non-negative and less than |m|. */
OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m);
/* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero
* on error. */
OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m, BN_CTX *ctx);
/* BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero
* on error. */
OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
BN_CTX *ctx);
/* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the
* same pointer. It returns one on success and zero on error. */
OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n,
const BIGNUM *m, BN_CTX *ctx);
/* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be
* non-negative and less than |m|. */
OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n,
const BIGNUM *m);
/* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the
* same pointer. It returns one on success and zero on error. */
OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
BN_CTX *ctx);
/* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be
* non-negative and less than |m|. */
OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a,
const BIGNUM *m);
/* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). |p| must be a
* prime. */
OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p,
BN_CTX *ctx);
/* Random and prime number generation. */
/* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero, the
* most-significant bit, if any, will be set. If |top| is one, the two most
* significant bits, if any, will be set.
*
* If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may
* not equal |bits| if the most significant bits randomly ended up as zeros.
*
* If |bottom| is non-zero, the least-significant bit, if any, will be set. The
* function returns one on success or zero otherwise. */
OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
/* BN_pseudo_rand is an alias for |BN_rand|. */
OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
/* BN_rand_range is equivalent to |BN_rand_range_ex| with |min_inclusive| set
* to zero and |max_exclusive| set to |range|. */
OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
/* BN_rand_range_ex sets |rnd| to a random value in
* [min_inclusive..max_exclusive). It returns one on success and zero
* otherwise. */
OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive,
const BIGNUM *max_exclusive);
/* BN_pseudo_rand_range is an alias for BN_rand_range. */
OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
/* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike
* BN_rand_range, it also includes the contents of |priv| and |message| in the
* generation so that an RNG failure isn't fatal as long as |priv| remains
* secret. This is intended for use in DSA and ECDSA where an RNG weakness
* leads directly to private key exposure unless this function is used.
* It returns one on success and zero on error. */
OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
const BIGNUM *priv,
const uint8_t *message,
size_t message_len, BN_CTX *ctx);
/* BN_GENCB holds a callback function that is used by generation functions that
* can take a very long time to complete. Use |BN_GENCB_set| to initialise a
* |BN_GENCB| structure.
*
* The callback receives the address of that |BN_GENCB| structure as its last
* argument and the user is free to put an arbitary pointer in |arg|. The other
* arguments are set as follows:
* event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime
* number.
* event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality
* checks.
* event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished.
*
* The callback can return zero to abort the generation progress or one to
* allow it to continue.
*
* When other code needs to call a BN generation function it will often take a
* BN_GENCB argument and may call the function with other argument values. */
#define BN_GENCB_GENERATED 0
#define BN_GENCB_PRIME_TEST 1
struct bn_gencb_st {
void *arg; /* callback-specific data */
int (*callback)(int event, int n, struct bn_gencb_st *);
};
/* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to
* |arg|. */
OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback,
int (*f)(int event, int n,
struct bn_gencb_st *),
void *arg);
/* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of
* the callback, or 1 if |callback| is NULL. */
OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n);
/* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe
* is non-zero then the prime will be such that (ret-1)/2 is also a prime.
* (This is needed for Diffie-Hellman groups to ensure that the only subgroups
* are of size 2 and (p-1)/2.).
*
* If |add| is not NULL, the prime will fulfill the condition |ret| % |add| ==
* |rem| in order to suit a given generator. (If |rem| is NULL then |ret| %
* |add| == 1.)
*
* If |cb| is not NULL, it will be called during processing to give an
* indication of progress. See the comments for |BN_GENCB|. It returns one on
* success and zero otherwise. */
OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
const BIGNUM *add, const BIGNUM *rem,
BN_GENCB *cb);
/* BN_prime_checks is magic value that can be used as the |checks| argument to
* the primality testing functions in order to automatically select a number of
* Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */
#define BN_prime_checks 0
/* BN_primality_test sets |*is_probably_prime| to one if |candidate| is
* probably a prime number by the Miller-Rabin test or zero if it's certainly
* not.
*
* If |do_trial_division| is non-zero then |candidate| will be tested against a
* list of small primes before Miller-Rabin tests. The probability of this
* function returning a false positive is 2^{2*checks}. If |checks| is
* |BN_prime_checks| then a value that results in approximately 2^{-80} false
* positive probability is used. If |cb| is not NULL then it is called during
* the checking process. See the comment above |BN_GENCB|.
*
* The function returns one on success and zero on error.
*
* (If you are unsure whether you want |do_trial_division|, don't set it.) */
OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime,
const BIGNUM *candidate, int checks,
BN_CTX *ctx, int do_trial_division,
BN_GENCB *cb);
/* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime
* number by the Miller-Rabin test, zero if it's certainly not and -1 on error.
*
* If |do_trial_division| is non-zero then |candidate| will be tested against a
* list of small primes before Miller-Rabin tests. The probability of this
* function returning one when |candidate| is composite is 2^{2*checks}. If
* |checks| is |BN_prime_checks| then a value that results in approximately
* 2^{-80} false positive probability is used. If |cb| is not NULL then it is
* called during the checking process. See the comment above |BN_GENCB|.
*
* WARNING: deprecated. Use |BN_primality_test|. */
OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks,
BN_CTX *ctx, int do_trial_division,
BN_GENCB *cb);
/* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with
* |do_trial_division| set to zero.
*
* WARNING: deprecated: Use |BN_primality_test|. */
OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks,
BN_CTX *ctx, BN_GENCB *cb);
/* Number theory functions */
/* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero
* otherwise. */
OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx);
/* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If |out| is NULL, a
* fresh BIGNUM is allocated. It returns the result or NULL on error.
*
* If either of |a| or |n| have |BN_FLG_CONSTTIME| set then the operation is
* performed using an algorithm that avoids some branches but which isn't
* constant-time. This function shouldn't be used for secret values, even
* with |BN_FLG_CONSTTIME|; use |BN_mod_inverse_blinded| instead. Or, if
* |n| is guaranteed to be prime, use
* |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking
* advantage of Fermat's Little Theorem. */
OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
const BIGNUM *n, BN_CTX *ctx);
/* BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the
* Montgomery modulus for |mont|. |a| must be non-negative and must be less
* than |n|. |n| must be greater than 1. |a| is blinded (masked by a random
* value) to protect it against side-channel attacks. |BN_mod_inverse_blinded|
* may or may not ignore the |BN_FLG_CONSTTIME| flag on any/all of its inputs.
* It returns one on success or zero on failure. On failure, if the failure was
* caused by |a| having no inverse mod |n| then |*out_no_inverse| will be set
* to one; otherwise it will be set to zero. */
int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
const BN_MONT_CTX *mont, BN_CTX *ctx);
/* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or
* 1), or -2 on error. */
OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
/* Montgomery arithmetic. */
/* BN_MONT_CTX contains the precomputed values needed to work in a specific
* Montgomery domain. */
/* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */
OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void);
/* BN_MONT_CTX_free frees memory associated with |mont|. */
OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont);
/* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
* NULL on error. */
OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
const BN_MONT_CTX *from);
/* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
* returns one on success and zero on error. */
OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod,
BN_CTX *ctx);
/* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If
* so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It
* then stores it as |*pmont|. It returns one on success and zero on error.
*
* If |*pmont| is already non-NULL then it does nothing and returns one. */
int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
const BIGNUM *mod, BN_CTX *bn_ctx);
/* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It
* returns one on success and zero on error. */
OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a,
const BN_MONT_CTX *mont, BN_CTX *ctx);
/* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values
* out of the Montgomery domain. It returns one on success or zero on error. */
OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a,
const BN_MONT_CTX *mont, BN_CTX *ctx);
/* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain.
* Both |a| and |b| must already be in the Montgomery domain (by
* |BN_to_montgomery|). It returns one on success or zero on error. */
OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a,
const BIGNUM *b,
const BN_MONT_CTX *mont, BN_CTX *ctx);
/* Exponentiation. */
/* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply
* algorithm that leaks side-channel information. It returns one on success or
* zero otherwise. */
OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
BN_CTX *ctx);
/* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best
* algorithm for the values provided and can run in constant time if
* |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero
* otherwise. */
OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx);
OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx,
const BN_MONT_CTX *mont);
OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx,
const BN_MONT_CTX *mont);
/* Deprecated functions */
/* BN_bn2mpi serialises the value of |in| to |out|, using a format that consists
* of the number's length in bytes represented as a 4-byte big-endian number,
* and the number itself in big-endian format, where the most significant bit
* signals a negative number. (The representation of numbers with the MSB set is
* prefixed with null byte). |out| must have sufficient space available; to
* find the needed amount of space, call the function with |out| set to NULL. */
OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out);
/* BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The
* bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|.
*
* If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise
* |out| is reused and returned. On error, NULL is returned and the error queue
* is updated. */
OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out);
/* BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is
* given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success
* or zero otherwise. */
OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx,
const BN_MONT_CTX *mont);
/* BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success
* or zero otherwise. */
OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
const BIGNUM *p1, const BIGNUM *a2,
const BIGNUM *p2, const BIGNUM *m,
BN_CTX *ctx, const BN_MONT_CTX *mont);
/* Private functions */
struct bignum_st {
BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian
order. */
int top; /* Index of last used element in |d|, plus one. */
int dmax; /* Size of |d|, in words. */
int neg; /* one if the number is negative */
int flags; /* bitmask of BN_FLG_* values */
};
struct bn_mont_ctx_st {
BIGNUM RR; /* used to convert to montgomery form */
BIGNUM N; /* The modulus */
BN_ULONG n0[2]; /* least significant words of (R*Ri-1)/N */
};
OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l);
#define BN_FLG_MALLOCED 0x01
#define BN_FLG_STATIC_DATA 0x02
/* avoid leaking exponent information through timing, BN_mod_exp_mont() will
* call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch,
* BN_mod_inverse() will call BN_mod_inverse_no_branch. */
#define BN_FLG_CONSTTIME 0x04
#if defined(__cplusplus)
} /* extern C */
#endif
#define BN_R_ARG2_LT_ARG3 100
#define BN_R_BAD_RECIPROCAL 101
#define BN_R_BIGNUM_TOO_LONG 102
#define BN_R_BITS_TOO_SMALL 103
#define BN_R_CALLED_WITH_EVEN_MODULUS 104
#define BN_R_DIV_BY_ZERO 105
#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106
#define BN_R_INPUT_NOT_REDUCED 107
#define BN_R_INVALID_RANGE 108
#define BN_R_NEGATIVE_NUMBER 109
#define BN_R_NOT_A_SQUARE 110
#define BN_R_NOT_INITIALIZED 111
#define BN_R_NO_INVERSE 112
#define BN_R_PRIVATE_KEY_TOO_LARGE 113
#define BN_R_P_IS_NOT_PRIME 114
#define BN_R_TOO_MANY_ITERATIONS 115
#define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116
#define BN_R_BAD_ENCODING 117
#define BN_R_ENCODE_ERROR 118
#endif /* OPENSSL_HEADER_BN_H */
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